Nabble - Graph Theory

algorithm for a weighted graph problem

2008-08-29T05:54:18Z

given a connected undirected graph with a positive weight assigned to each unordered pair of vertices and length assigned to each edge, find a connected sub graph
with X minimized, where X is

Re: Polynomial algorithm for graph isomorphism?

2008-06-26T15:07:56Z

I though to search for counterexamples among cospectral graphs, Ted Spence and Gordon Royle advised me to check strongly regular graphs:
http://www.maths.gla.ac.uk/~es/srgraphs.html
And ... all of them are counterexamples to all algorithms I've proposed...
These invariants even doesn't recognize orbits for these graphs... they seem to be copletely resistant to combinatorial type invariants... which makes that I've started to doubt about that polynomial isomorphism is polynomial...

Re: Polynomial algorithm for graph isomorphism?

2008-06-18T08:20:09Z

Above invariants creates some blocking of vertexes with the same invariants - it's topological property.
There will be always vertexes which are indistinguishable - for which there is automorphism transforming one into the other (which are in the same orbit), the question is if our blocking is blocking into orbits? And if the invariants determine uniquely transitive graphs (all vertexes have the same invariants)?

To create more invariants for vertex(i), we can take non diagonal elements of powers of the matrix, and forget about their order - sort them lexicographically. We can make it even smarter - use already found blocking - to the description of neighbor j {((A^k)_ij):k} include also the number of its block. Thanks of it we can find better blocking ... use it to get better ... it will stabilize in polynomial time.
Finally we have all powers of adjacency matrix, but without exact permutation of terms inside some blocks. The permutation inside the block can be freely chosen, so we can assume that we know exactly the first lines of powers of the matrix for each block.

Finally we for example have: diagonal and the first line of powers of the matrix: n^2 + n(n-1) polynomial equations for elements of symmetric matrix ( n(n-1)/2 terms).
We know that there is solution. The question is if is always unique?

Polynomial algorithm for graph isomorphism?

2008-04-28T23:00:48Z

There are n^2 invariants for graphs, which can be computed in polynomial time - diagonal terms of n different powers of the adjacency matrix.
They tells the number of closed path from the vertex of given length - for example diagonal of second power gives degrees of vertexes (for unoriented graph). Higher powers describes vertex local topology deeper.
Now vectors of these invariants for different vertexes can be sorted lexicographically, giving n^2 invariants up to isomorphism.

So if these invariants doesn't agree for two graphs - the aren't isomorphic.
But question is if the invariants agree, they are isomorphic.
I've showed that it should be in generic case:
http://front.math.ucdavis.edu/0804.3615v1

I'm looking for a counterexamples - two non isomorphic graphs with the same invariants.
How to look for them? Maybe there are none?

thanks
Jarek Duda

CFP: Nano-Net 2008

2008-03-08T15:51:50Z

CFP: Nano-Net 2008

2008-03-08T14:55:57Z

**************** Nano-Net 2008 *********************

CALL FOR PAPERS

3rd International Conference on Nano-Networks
Boston, USA, Sept 15-17, 2008

http://www.nanonets.org

Sponsors: Create-Net, ICST, EU (IST-FET), ENIAC
Industry Sponsor: STMicroelectronics

*****************************************************
For RSS feed on conference updates, register: http://nano-net.blogspot.com/feeds/posts/default.

SCOPE: The Nano-Net conference positions itself at the intersection of two worlds, namely, emerging nanotechnologies on one-side, and network/communication theory on the other side. The standing question that this conference will address is: What are the new communication paradigms that derive from the transition from micro- to nano-scale devices? The related degrees of freedom and constraints associated with these new technologies will change our notions about efficient network and system design. Nano-Net provides a multidisciplinary forum for the discussion of new techniques in modeling, design, simulation, and fabrication of network and communication systems at the nano-scale.

PAPERS: The conference invites original technical papers that have not been previously published and are not currently under review for publication elsewhere. Contributions addressing all subjects pertaining to nanotechnology & networking are solicited. Suggested topics include, but are not limited to, the following:

* Applications for Nano-Networks

Wireless nanoscale transmitters and receivers, nano-sensors and actuators, nanorobotics, medical and in-vivo imaging and sensing, lab on a chip, swarm micro and nano-inspection, embedding sensing, etc...

* Modeling, Simulation, Standards and Architectural Aspects of Nano-Networks

Physical characterization/modeling of nano-scale interconnects and devices, Fault-tolerant and reliability of nano-devices, Self-healing properties of nano-networks, CAD flows for NoCs and MP-SoC platforms, NoC performance and trade-off analysis, Energy efficiency, Bio-inspired aspects

* Novel Information and Graph Theory Aspects of Nano-Networks

Network architectures and topologies, Statistical mechanics approach to nano-communications, Routing/addressing issues in nano-networks, Nano-coding, Applications of complex network theory, Self-organization in nano-scale systems, Modeling of Nano/Bio Communication Channels

* Device Physics and Interconnects

Nano-technologies and devices for on-chip interconnects (CNTs, graphene nano-ribbons, semic., metallic and DNA-templated nanowires), Molecular, optical and wireless interconnects, Interconnects for non-charge-based devices, emerging 3D-interconnect technologies

* Nano-Robotics

Communication systems and networking protocols for sub-inch robotic systems, including low-bandwidth coordination schemes for nano-robot teams and range and bearing devices for inter-robot relative positioning

* Bio-nano Applications

Bio-Micro/Nanoelectronics, Molecular scale chemical and biosensors, Bio-MEMS technology, Data and power management, Nano-scale and molecular communications and information processing, Information theory analysis of biological communications, Molecular Computation using molecular cells, Chemical computing

SUBMISSION INSTRUCTIONS: Prospective authors are encouraged to submit a PDF version of the full paper in English. Papers are limited to 5 two-column pages, in a font no smaller than 10-points. Style guides and further information are available on the conference website: http://www.nanonets.org. Presentation will be either oral or in poster format, as deemed appropriate by the Technical Program Committee.

PUBLICATION: All submitted papers will be subject to a rigorous peer-review. Accepted papers will be published by Springer in the Nano-Net Conference Proceedings, and made available online through Springer Lecture Notes in Computer Science (LNICST). Selected high-quality papers with a strong nanoscale device component will be reviewed for a Special Issue of the IEEE Transactions on Nanotechnology, in an extended version.

WORKSHOP & TUTORIAL PROPOSALS: Proposals for Special Sessions and Tutorials are encouraged. Potential Workshop and Tutorial organizers should submit a proposal of at most 5 pages, including scope/motivation of the session/tutorial, list of invited papers (still subject to peer-review) and short-bio of the organizer(s). Workshops should be submitted by e-mail to: goel@albany.edu, tutorials to: liyun@research.ge.com.

IMPORTANT DATES
===============
Workshop Proposals: May 2, 2008
Paper Submissions: May 15, 2008
Acceptance Notification: June 30, 2008
Camera-Ready Version: July 31, 2008
Nano-Net Conference: Sept. 15-17, 2008

Program Chairs
==============
GENERAL CHAIR
Stephen F Bush
bushsf@research.ge.com
General Electric, USA

TECHNICAL PROGRAM CHAIR
Alexandre Schmid
EPFL, Switzerland

TECHNICAL PROGRAM CO-CHAIRS
Alexander Sergienko
Boston University, USA

Kaustav Banerjee
UCSB, USA

Radu Marculescu
CMU, USA

Sumit Roy
U Washington, USA

Nikolaus Correll
MIT, USA

Tatsuya Suda
UC Irvine, USA

Sasitharan Balasubramaniam
TSSG, Ireland

STEERING COMMITTEE
Imrich Chlamtac (Chair)
Create-Net, Italy

Gian Mario Maggio
Create-Net, Italy

WORKSHOP CHAIR
Sanjay Goel
UAlbany, USA

TUTORIAL CHAIR
Yun Li
General Electric, USA

STANDARDS CHAIR
Dan Gamota Motorola, USA

PUBLICATIONS CHAIR
Maggie Cheng
Missouri S&T, USA

FINANCE CHAIR
Karen Decker
ICST

LOCAL ARRANGEMENTS CHAIR
Neil Gershenfeld MIT, USA

WEBMASTER
Damira Pon
UAlbany, USA

CONFERENCE COORDINATOR
Dorothy Bany
ICST

maximum weighted matching in graphs

2008-02-20T21:46:36Z

hi,
does anyone know a maximum weighted matching algorithm for undirected non bipartite graphs. I want to implement it in java.pl........ help
bye!

TMFCS-08 Final Call for papers

2008-01-16T11:19:30Z

Final Call for papers

The 2008 International Conference on Theoretical and Mathematical Foundations of Computer Science (TMFCS-08) (website: www.PromoteResearch.org ) will be held during July 7-10 2008 in Orlando, FL, USA. We invite draft paper submissions and the deadline for paper submission is just few weeks from now. The conference will be held at the same time and place where several other major events are taking place. The website contains more details.

Sincerely
John Edward

Convex graph ???

2008-01-08T02:00:19Z

Hi,

I saw the term "convex graph" in an article. I know what means "convex
function" but in graph theory, I have any idea what means "convex graph".
Does anyone have a definition for this term?

Thank you,

Searching for all the induced cycles in a graph

2007-12-28T14:48:37Z

Hi there!

First of all I want to say that I'm not a mathematician and hope I will make myself clear.

My problem is the following: I have a planar graph G which doesn't have any bridges. For that graph I want to find the set of all induced cycles. I researched a bit on the terminology and I think those are the correct terms for what I have and want to do. I'm wondering if the problem is really NP-Hard and if there's any heuristics that can help me find the problem. Besides the graph I have some more information about it that might help: some of the paths in the graph are actually 1 degree curves. Said in other way, I have a bunch of 1 degree lines that intersect with each other and I want to find all those "small and independent" loops they define.
Can anyone give me at least some clues/directions on where to get a good solution for it?

what kind of topics on graph

2007-12-18T04:44:07Z

hello,

now i am doing final project 4 my graduate from university..

and the title of my project is interactive teaching modul of graph Theory

i've some quetions coz i dont really know about graph theory..

could u help me??

1. what kind of primary topics on graph theory which have to be shown on my interactive modul?? coz im so confused bout topics on graph theory,, there are so many more topics right??

so what should i do?? what do you think? what are the important or primary topics which is explained??

thanks 4 ur attention..

Graph Theory characteristic polynomial problem

2007-10-15T23:18:06Z

This is a problem I'm having difficulty solving completely. It concerns a
graph of m vertices with at least one vertex of degree m-1, which is
neccessarily connected so its incidence matrix has rank m-1.

(i) If one considers an incidence matrix, Phi, over a field of
characteristic 0, ie the incidence matrix of a directed graph where the
columns correspond to the edges and each column contains exactly one 1,
one -1, and remaining entries 0, (all zeroes for a loop). Any assignment of
edge orientations is acceptable here.

Now forming the Gram matrix, Phi Phi', for the type of graph above one
obtains the characteristic polynomial,

p(x) = x(a0 + a1 x + a2 x^2 + ... + x^m-2)(x-m)

where a0 = number of spanning trees = the product of the roots of the middle
factor.

The roots for this type graph seem always to be integers (for the few
examples I've tried), but I haven't been able to prove this.

(ii) Second this polynomial seems to be related to another characteristic
polynomial of a full rank ExE matrix that describes the system of
fundamental cut sets and cycles of the graph relative to any given spanning
tree.

The formation of this matrix is involved:
1. Let Phi(i) be obtained by deleting the ith row.

2. Let G = -[(Phi(i)A' )^(-1)] [Phi(i)B'] where A' selects the columns of
Phi corresponding the branches of a given spanning tree, and B' selects the
columns corresponding to the chords. G then is |T|x|T^C| and describes the
system of fundamental cuts and cycles.

3. Form the full rank ExE matrix, Theta = I + (A'GB - B'G'A) = I + S, where
the second terms on the right are skew symmetric. This is another way of
describing the system of fundamental cuts and cycles of a given spanning
tree. I was able to show that the determinant of Theta is the number of
spanning trees by induction on the number of edges.

Now the characteristic polynomial of S has the form

f(y) = y^k(c0 + c2 y^2 + c4 y^4 + ... + y^2n)

where E = 2n + k and the the sum of the coefficients
c0 + c1 + c4 + ... + 1 is the number of spanning trees.

If we rewrite the second factor as

h(x) = c0 + c1 x + c2 x^2 + ... + x^n

and pad h(x) with enough zero roots if neccessary so that its degree is m-2
where m is the number of vertices, then in regards to (i) above

p(x) = x h(1-x) (x-m)

But I can't prove this nor can I show that the roots of h(x) are also always
integers. Also we only have m-1 <= 2n+k <= m(m-1)/2, but this admits the
possibility that n > m-2 and in the few examples I've tried this never
happens. I've haven't tried many examples though.

I've posted a paper I've written,
http://www.bcpl.net/~smkauffm/gtlawatersigned.pdf , which discusses these
two seemingly related polynomials in section 5.1 page 18, and section 7.1
page 37.

Any ideas, or where the problem has been treated before?
--
Stephen Kauffman
strangerland@gmail.com
http://himthealmightypowerhurled.blogspot.net

Nursing Jobs

2007-02-28T18:31:08Z

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Question on graph theory

2006-11-22T21:52:21Z

Four schools P,Q,R and S each has team A and team B in a tournament. The teams from the same school do not play against each other. At certain stage of the tournament, the numbers of games played by the teams, except team A of school P, are distinct. Determine the number of games played by team B of school P.

3 steps to money!!!

2006-11-07T01:53:51Z

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Grid

2006-11-02T14:55:37Z

Is there a name for an "n x n" grid with edges added so that it is 4-regular, non-planar. So all variables have an adjacent neighbor above, below and to its left and right. For vertices on the perimeter of degree 3 one edge is added linking it with its symmetrically equivalent perimeter vertex, i.e. if a vertex at the top of the grid has degree 3 then an edge is added linking it to the vertext at the bottom of its column of vertices in the graph, similarly for rows.
So there are 2*n edges added to a normal "n x n" grid to make it so every vertex is of degree 4.
I am trying to find out if there is a specific name for such a "grid"?

Re: What's kind of graph?

2006-02-01T13:33:03Z

Hi

Thank you very much for your reply.

Please wait... I will be back with this question again.

OK?

thanks

Graph Component

2006-01-31T21:17:21Z

I've some doubts in graph components.
The question as given below. See if you can give me some insight.
Thnx

Re: What's kind of graph?

2006-01-31T21:05:28Z

Supeeti
I'm not sure if u still need a solution to this problem.
If so let me know your requiremnts in detail .
If you can make it more clear what is the requirement of your final graph?

thnx

What's kind of graph?

2005-12-08T07:51:37Z

Hi all,

I have some problems with something that may be called "graph".
My program produces the results that look like the picture as follow

In this picture, there are 4 results which each result is composed of data node. There is only one direction from left to right, no loop.

The first question is, what kind of this graph? Directed graph or else?

Afther I have the results. I need to do something to get new result like the picture as following. Someone said me "factorize", I don't know.

So, the second quesiton, Which technique or algorithm or methodology are used for "factorize".

thanks